How to compare performance of robust design optimization algorithms, including a novel method

Abstract This paper proposes a method to compare the performances of different methods for robust design optimization of computationally demanding models. Its intended usage is to help the engineer to choose the optimization approach when faced with a robust optimization problem. This paper demonstrates the usage of the method to find the most appropriate robust design optimization method to solve an engineering problem. Five robust design optimization methods, including a novel method, are compared in the demonstration of the comparison method. Four of the five compared methods involve surrogate models to reduce the computational cost of performing robust design optimization. The five methods are used to optimize several mathematical functions that should be similar to the engineering problem. The methods are then used to optimize the engineering problem to confirm that the most suitable optimization method was identified. The performance metrics used are the mean value and standard deviation of the robust optimum as well as an index that combines the required number of simulations of the original model with the accuracy of the obtained solution. These measures represent the accuracy, robustness, and efficiency of the compared methods. The results of the comparison show that sequential robust optimization is the method with the best balance between accuracy and number of function evaluations. This is confirmed by the optimizations of the engineering problem. The comparison also shows that the novel method is better than its predecessor is.

[1]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[2]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[3]  Jürgen Branke,et al.  Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation , 2006, IEEE Transactions on Evolutionary Computation.

[4]  Raphael T. Haftka,et al.  Improved Global Convergence Probability Using Independent Swarms , 2005 .

[5]  M. J. Box.  A New Method of Constrained Optimization and a Comparison With Other Methods , 1965, Comput. J..

[6]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007, DAC 2006.

[7]  Larsgunnar Nilsson,et al.  Robust optimization of front members in a full frontal car impact , 2013 .

[8]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[9]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[10]  Petter Krus,et al.  Performance index and meta-optimization of a direct search optimization method , 2013 .

[11]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[12]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

[13]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[14]  Patrick H. Reisenthel,et al.  A Numerical Experiment on Allocating Resources Between Design of Experiment Samples and Surrogate-Based Optimization Infills , 2011 .

[15]  Xiaoping Du,et al.  The use of metamodeling techniques for optimization under uncertainty , 2001 .

[16]  Neculai Andrei,et al.  An Unconstrained Optimization Test Functions Collection , 2008 .

[17]  Robert E. Mercer,et al.  ADAPTIVE SEARCH USING A REPRODUCTIVE META‐PLAN , 1978 .

[18]  Xiaolong Feng,et al.  Multidisciplinary Design Optimization of Modular Industrial Robots by Utilizing High Level CAD Templates , 2012 .

[19]  Fred van Keulen,et al.  Efficient Kriging-based robust optimization of unconstrained problems , 2014, J. Comput. Sci..

[20]  Antonius H. van den Boogaard,et al.  Sequential robust optimization of a V-bending process using numerical simulations , 2012, Structural and Multidisciplinary Optimization.

[21]  Yoel Tenne,et al.  An adaptive-topology ensemble algorithm for engineering optimization problems , 2015 .

[22]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[23]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[24]  Johan Ölvander,et al.  Comparison of Different Uses of Metamodels for Robust Design Optimization , 2013 .

[25]  Massimiliano Gobbi,et al.  A local approximation based multi-objective optimization algorithm with applications , 2014 .

[26]  Andy J. Keane,et al.  Non-stationary kriging for design optimization , 2012 .

[27]  Johan Ölvander,et al.  Optimization of the Complex-RFM optimization algorithm , 2015 .

[28]  R. F. Coelho.  Metamodels for mixed variables based on moving least squares , 2014 .

[29]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[30]  Petter Krus,et al.  Optimizing the Optimization - A Method for Comparison of Optimization Algorithms , 2006 .

[31]  Johan Ölvander,et al.  Comparison of Sampling Methods for a Dynamic Pressure Regulator , 2011 .

[32]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.